Lithiation of hydrothermally synthesized Li1-xFex(OH)Fe1-ySe turns on high-temperature superconductivity when iron ions are displaced from the hydroxide layers by reductive lithiation to fill the vacancies in the iron selenide layers. Further lithiation results in reductive iron extrusion from the hydroxide layers, which turns off superconductivity again as the stoichiometric composition Li(OH)FeSe is approached. The results demonstrate the twin requirements of stoichiometric FeSe layers and reduction of Fe below the +2 oxidation state as found in several iron selenide superconductors.